I tried to solve a question which led

Ean Hughes

Ean Hughes

Answered question

2022-04-06

I tried to solve a question which led to
4sinπ5sin3π5=5

Answer & Explanation

Jax Burns

Jax Burns

Beginner2022-04-07Added 13 answers

Note that
sin3π5=sin2π5
then use a double-angle and triple-angle forumla:
sin2x=2sinxcosx
sin3x=3sinx4sin3x
In this case, x=π5. Setting the above two equations equal to each other results in the quadratic equation in question:
2cosx=34(1cos2x)=4cos2x1
which means that
cosx=1+54
sinx=10254
Then, using sin2x=sin3x as noted above, we have
4sinxsin2x=8sin2xcosx=81025161+54
=101025+1058=5

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